Strain and molecular mechanics

The mathematical expressions for the force Aelds are derived from classical-mechanical potenAal energy funcAons. The energy required to stretch a bond or to bend a bond angle increases as the square of the distortion. For bond stretching, 

The torsional strain is a sinusoidal function of the torsion angle. Torsional strain results from the barrier to rotation about single bonds as described for ethane on p. 56. For molecules with a threefold barrier such as ethane, the form of the torsional barrier is 

The populations of the various conformations are related to the energy between them by the equation 

This corresponds to a distribution of 66% anti and 34% gauche. Table 3.2 gives the relationship between free-energy difference, equilibrium constant, and percent composition of a two-component mixture. 

Examples of attractive nonbonded interactions can be found in certain halogenated hydrocarbons. In 1-chloropropane, for example, the gauche ccMiformation is slightly 

Potential energy diagram for rotation about C(2)—C(3) bond of n-butane 

---

Table 3.3. Correlation between Intramolecular Strain from Molecular Mechanics (MM) Calculations and Activation Energies for Dissociation of C—C Bonds in Substituted Ethanes"...

The calculations described here have been called strain calculations, molecular mechanics, or force field calculations. We prefer the latter term. For a discussion of historical developments and a literature survey of earlier work, which are not given here, the reader is referred to a number of other reviews (1-3). The present paper deals with the description of force field types, techniques of energy minimisation, and procedures for the determination of force field parameters, and with some applications, preferentially taken from our own field of interest. In accordance with the experiences of the author, the work of Lifson and coworkers is given special attention other authors are nevertheless well represented in the context of critical comparisons. We hope that this selection, although inevitably biased, will help to improve the consistency of the presentation of the subject. 

Semiempirical and molecular mechanics calculations have been widely used. Thus, conformation of indolo benzazepine 423 (Figure 8) with its conjugated benzo and indole rings has been studied by molecular mechanics (MMX force field). Its planarity was estimated from a calculation of dihedral angle Ti 2 3 4 the value of ca. 22° is due to strain as contributed by azepine ring. This characteristic was further compared to that of the open-chain and six-membered... 

Several approaches are being explored and developed using new methods in biotechnology to eliminate pre-harvest aflatoxin contamination of food and feed. These approaches resulted from recent information acquired on 1) non-aflatoxigenic A. flavus strains that prevent aflatoxin contamination of cottonseed when co-inoculated with aflatoxigenic strains, 2) molecular mechanisms governing aflatoxin biosynthesis, and 3) plant-derived metabolites that inhibit aflatoxin biosynthesis. 

In this section we will discuss in some detail the relationship between molecular mechanics force field parameters and real physical parameters. As mentioned before, the fundamental difference between spectroscopic and molecular mechanics force fields is that the former are molecule-specific while the latter are general. Empirical force field parameters can be used for the calculation of unknown structures and their strain energies, and for the prediction of vibrational frequencies of new compounds. However, the parameters themselves generally have limited meaning. 

There has been a decisive evolution in the treatment of steric effects in heteroaromatic chemistry. The quantitative estimation of the role of steric strain in reactivity was first made mostly with the help of linear free energy relationships. This method remains easy and helpful, but the basic observation is that the description of a substituent by only one parameter, whatever its empirical or geometrical origin, will describe the total bulk of the substituent and not its conformationally dependent shape. A better knowledge of static and dynamic stereochemistry has helped greatly in understanding not only intramolecular but also intermolecular steric effects associated with rates and equilibria. Quantum and molecular mechanics calculations will certainly be used in the future to a greater extent. 

Evaluation of the strain energy in SPC was a subject of numerous calculations, which provided substantially different results. Unfortunately, very limited experimental data on the heats of formation of these compounds preclude the evaluation of the validity of the calculations. The results of nonempirical (4-31G//STO-3G) and molecular mechanics (MM2) calculations were in reasonable agreement with experimental data, while the semiempiri-cal methods resulted in substantial deviations. Even better results were obtained by Aped and Allinger using the MM3 method Available experimental data on the heats of formation of SPC and matching calculated values are collected in Table 1. 

C8-C13 ether bridge spans two axial sites of the cis-fused octalin system, and molecular mechanics calculations predict a relatively strain-fiee tricyclic array. Based on these observations, our initial strategic considerations focused on approaches in which the nargenicin ether bridge would be established by intramolecular addition of C8 or C13 alcohols to complementary electrophilic sites at C13 or C8 (Figure 10). The diaxial orientation of the vicinal oxygens at C8 and C9 further suggested that intramolecular addition to a C8-C9 epoxide would serve as an efficient vehicle for tricycle construction with concurrent development of C9 stereochemistry. 

---